Critical points and Warped product metrics
Bull. Korean Math. Soc. 2004 Vol. 41, No. 1, 117-123
Published online March 1, 2004
Seungsu Hwang, Jeongwook Chang
Chung-Ang University and Konkuk University
Abstract : It has been conjectured that, on a compact orientable manifold $M$, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a $3$-dimensional warped product, then $(M,g)$ cannot be a critical point unless it is isometric to the standard sphere.
Keywords : total scalar curvature functional, critical point equation, Einstein metric
MSC numbers : 52C25
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